| Preface |
|
i | |
| Notation |
|
1 | (4) |
| Introduction |
|
5 | (14) |
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Dirichlet Characters and Gauss Sums |
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|
19 | (9) |
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19 | (2) |
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21 | (7) |
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Estimations of Character Sums |
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|
28 | (13) |
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Estimation of simplest character sum |
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28 | (2) |
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30 | (2) |
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Classical mean value estimations |
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32 | (2) |
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34 | (2) |
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New mean value estimations |
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|
36 | (5) |
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Mean Value Estimates for Riemann Zeta Function and Dirichlet L-Functions |
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41 | (15) |
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42 | (5) |
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Mean value estimates for ζ4(s) |
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47 | (4) |
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Hybrid mean value estimates for L4(s, x) |
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51 | (3) |
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Mean value estimates for L2(s, x) |
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54 | (2) |
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Distributions of Zeros (A) |
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56 | (12) |
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Zero-density theorems of L-functions |
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57 | (6) |
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An improvement of the zero-density theorem of zeta function |
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63 | (5) |
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Estimates of Linear Trigonometric Sums with Prime variable |
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68 | (22) |
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68 | (10) |
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78 | (4) |
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82 | (6) |
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Estimate of linear trigonometric sum with prime variable for small q |
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88 | (2) |
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Goldbach-Vinogradov Theorem |
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90 | (19) |
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90 | (2) |
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92 | (4) |
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96 | (3) |
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Representation of large odd integer as a sum of three almost equal primes |
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99 | (2) |
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101 | (8) |
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109 | (31) |
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109 | (4) |
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The simplest Selberg upper bound method |
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113 | (3) |
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The functions G1 (ξ, z) and G1(z) |
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116 | (7) |
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Two fundamental theorems of estimating the sifting function |
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123 | (3) |
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The functions F(u) and f(u) |
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126 | (5) |
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131 | (9) |
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Mean Value Theorems of the Distribution of Primes in Arithmetical Progressions |
|
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140 | (18) |
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Bombieri-Vinogradov theorem |
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141 | (3) |
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144 | (9) |
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153 | (5) |
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158 | (14) |
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158 | (6) |
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164 | (8) |
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Distributions of Zeros (B) |
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172 | (18) |
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Several Lemmas of Dirichlet L-functions |
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172 | (3) |
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175 | (4) |
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Deuring-Heilbronn phenomenon |
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179 | (6) |
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Linnik's zero-density theorem |
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185 | (5) |
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190 | (24) |
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The elementary estimation of E(x) |
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190 | (5) |
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The further estimation of E(x) |
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195 | (13) |
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Goldbach numbers in small intervals |
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208 | (6) |
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214 | (7) |
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215 | (3) |
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218 | (3) |
| Appendix Two Remarks on the Binary Goldbach Conjecture |
|
221 | (9) |
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Remark I. The main term of the binary Goldbach conjecture |
|
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222 | (3) |
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Remark II. The integral on the supplementary intervals |
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|
225 | (5) |
| Epilogue |
|
230 | (1) |
| References |
|
231 | (9) |
| Index |
|
240 | |
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